Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the geometry of half lightlike submanifolds $M$ of a semi-Riemannian manifold $\widetilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\widetilde{M}$ is tangent to $M$, the screen distribution on $M$ is totally umbilical in $M$ and the co-screen distribution on $M$ is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of $M$ is parallel.

Keywords: half lightlike submanifold, semi-Riemannian manifold with semi-symmetric non-metric connection, totally umbilical screen distribution

MSC numbers: Primary 53C25, 53C40, 53C50